AP EAMCET · Maths · Properties of Triangles
Let \(\triangle\) denote the area of a \(\triangle A B C\). If \(\alpha, \beta, \gamma\) are the lengths of the altitudes of the \(\triangle A B C\), then \(\alpha^{-2}+\beta^{-2}+\gamma^{-2}=\)
- A \(\frac{4}{\Delta}(\tan A+\tan B+\tan C)\)
- B \(\frac{1}{\Delta}(\cot A+\cot B+\cot C)\)
- C \(\frac{\Delta^2}{2}(\tan A+\tan B+\tan C)\)
- D \(\frac{\Delta^2}{4}(\cot A+\cot B+\cot C)\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\Delta}(\cot A+\cot B+\cot C)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Since, } \alpha^{-2}+\beta^{-2}+\gamma^{-2}=\frac{a^2}{4 \Delta^2}+\frac{b^2}{4 \Delta^2}+\frac{c^2}{4 \Delta^2} \\ & =\frac{a^2+b^2+c^2}{4 \Delta^2} \\ & =\frac{\left(a^2+b^2-c^2\right)+\left(b^2+c^2-a^2\right)+\left(c^2+a^2-b^2\right)}{4\left(\frac{a…
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